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CLS601S- CALCULUS 2- JAN 2020 |
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NAMIBIA UNIVERSITY
OF SCIENCE AND TECHNOLOGY
FACULTY OF HEALTH AND APPLIED SCIENCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
QUALIFICATION: Bachelor of science; Bachelor of science in Applied Mathematics and Statistics
QUALIFICATION CODE: 07BSOC; 07BAMS
LEVEL: 6
COURSE CODE: CLS601S
COURSE NAME: CALCULUS 2
SESSION: JANUARY 2020
DURATION: 3 HOURS
PAPER: THEORY
MARKS: 100
SECOND OPPORTUNITY/SUPPLEMENTARY EXAMINATION QUESTION PAPER
EXAMINER
Dr N. CHERE
MODERATOR:
Dr V. KATOMA
INSTRUCTIONS
Answer ALL the questions in the booklet provided.
Show clearly all the steps used in the calculations.
3. All written work must be done in blue or black ink and sketches must
be done in pencil.
,
PERMISSIBLE MATERIALS
1. Non-programmable calculator without a cover.
THIS QUESTION PAPER CONSISTS OF 3 PAGES (Including this front page)
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1.1. Let f(x)= 2+6x—3x?. Then
1.1.1. find the average value of fon [0, 1]
[3]
1.1.2. find a point c on [0, 1] such that f,y. = f(c).
[5]
1.2. | Determine whether the following sequence converges or diverges. If it converges
determine where it converges.
1.2.1 fy
[4]
1.2.2. (F
[4]
1.2.3. fey
[4]
1.3. Let f(x) =e~* . Then determine the third order Taylor polynomial approximation off about
x=0.
[7]
1.4. Let G(x) = fe vi + t* dt. Use the fundamental theorem of calculus to find G’(x).
[6]
1.5. Evaluate the following indefinite integrals.
1.5.1. f ex—e-X dx
[Use integration by substitution]
[4]
eX+e7X
1.5.2. x7? Inx dx
[Use integration by parts.]
[6]
1.6. Evaluate the following definite integrals.
1.6.1. f° (3x? + 2x +5) dx
[4]
2
1.6.2. [rs sin (<) dx
[use integration by substitution.]
[6]
1.7. Determine whether the following series converges or diverges. If it converges find the sum.
1.7.1. E25 (2): - (2))
[11]
1.7.2. Ygco ea(—1)"1
[4]
1.8. Find the interval of convergence and radius of convergence for the power series
Lk=t (pxa-1)*
[10]
1.9. Consider the region enclosed by the curves y = 2x, y = x?.Then
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1.9.1.
1.9.2.
1.9.3.
find the area of the region enclosed by the curves y = 2x, y= x”.
[6]
find the center of mass of the lamina enclosed by the region
y=2x, y= x?
[7]
find the volume of the solid generated when the region between the curves f(x) = x?
and g(x) = 2x revolved about the x-axis.
[4]
1.10. Use the Trapezoidal rule to approximate fovx + Inx withn=6.
[5]
END OF EXAMINATION